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Math Help - please check my working, trig indentity proof

  1. #1
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    please check my working, trig indentity proof

    Can someome please check my working and tell me if it is 'correct'. As my book shows a different method.

    using  cos2A = 2cos^{2}A - 1 = 1-2sin^{2}A

    show that;  cos^{2}\frac{x}{2} = \frac{1+cosx}{2}

    my method;

     cosx = cos2\frac{x}{2} = 2cos^{2}\frac{x}{2}-1

     \frac{1+ 2cos^{2}\frac{x}{2}-1}{2} The one's cancel, and I get

     \frac{2cos^{2}\frac{x}{2}}{2}

    and now can I cancel the two's to give me

     cos^{2}\frac{x}{2}

    or do I have to cancel both 'two's at the top?

    thanks
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  2. #2
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    Quote Originally Posted by Tweety View Post
    Can someome please check my working and tell me if it is 'correct'. As my book shows a different method.

    using  cos2A = 2cos^{2}A - 1 = 1-2sin^{2}A

    show that;  cos^{2}\frac{x}{2} = \frac{1+cosx}{2}

    my method;

     cosx = cos2\frac{x}{2} = 2cos^{2}\frac{x}{2}-1

     \frac{1+ 2cos^{2}\frac{x}{2}-1}{2} The one's cancel, and I get

     \frac{2cos^{2}\frac{x}{2}}{2}

    and now can I cancel the two's to give me

     cos^{2}\frac{x}{2}

    or do I have to cancel both 'two's at the top?

    thanks
    You got to \cos{2\left(\frac{x}{2}\right)} = 2\cos^{2}\frac{x}{2}-1

    \cos{x} = 2\cos^2{\frac{x}{2}} - 1

    \cos{x} + 1 = 2\cos^2{\frac{x}{2}}

    \frac{\cos{x} + 1}{2} = \cos^2{\frac{x}{2}}.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    You got to \cos{2\left(\frac{x}{2}\right)} = 2\cos^{2}\frac{x}{2}-1

    \cos{x} = 2\cos^2{\frac{x}{2}} - 1

    \cos{x} + 1 = 2\cos^2{\frac{x}{2}}

    \frac{\cos{x} + 1}{2} = \cos^2{\frac{x}{2}}.
    Thanks, I understand what you did, however I dont quite understand what I did wrong?

    could you please show/point out to me? cause both methods 'looks' valid to me, is it the last part where I cancel 2?

    thanks.
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  4. #4
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    Hello Tweety
    Quote Originally Posted by Tweety View Post
    Thanks, I understand what you did, however I dont quite understand what I did wrong?

    could you please show/point out to me? cause both methods 'looks' valid to me, is it the last part where I cancel 2?

    thanks.
    There's nothing wrong with your original method. You cancelled the 2's correctly.

    Grandad
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  5. #5
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    Thanks.
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